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I posted here regarding sources for Roberts's Law.

In this paper it gives a clear qualification of what Roberts's law is. (Page 9, ...Cross-sectional prediction..)

..In a given year, the compensation of a CEO is proportional to the size of the firm to the power of 1/3, S(n)1/3, an empirical relationship sometimes called Roberts’ (1956) law.

This gives us the following formula:

$ Pay$~$Size^b$ with $b ≃ 1/3. $

I could not find much info on how to calculate firm size so I dug around and found another paper titled "What Determines Firm Size? "

I found that there was an equation given and explained on page 10.

The average firm size in each size bin is first calculated by dividing the number of employees by the number of firms. The average size for the entire sector is then calculated as the weighted sum of these bin averages, using as weights the proportion of the total sectoral employment in that bin. This produces a “employee-weighted” average of firm size.

Employee Weighted Average Number of Employees =$${\sum_{bin=1}^n}(\frac{N^{Emp}_{bin}}{N^{Emp}_{Sector}})(\frac{N^{Emp}_{bin}}{N^{Firm}_{bin}})$$

Emp bin is the total number of employees in a bin, N Emp Sector is the total number of employees in the sector, and NFirms bin is the total number of firms in a bin. In contrast to the firm-weighted simple average, the employee-weighted average emphasizes the larger firms; note the squaring of bin employment in the numerator.

Robert's law is now:

$$Pay={\sum_{bin=1}^n}\left[\left(\frac{N^{Emp}_{bin}}{N^{Emp}_{Sector}})(\frac{N^{Emp}_{bin}}{N^{Firm}_{bin}}\right)\right]^{b}$$ Now I am aware I'm kinda just copying and pasting and my research may be incorrect. But i'd like some data to test Roberts's law.

Where can I find data on CEO pay and company information?

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  • $\begingroup$ I'm not convinced that differences in employee counts in the firm cross-section without adjustments for output levels represent only differences in firm size, could just represent differences in labor intensity of the production process. Does anyone use any other firm size measures like market cap or perhaps some real output measures? There are other concerns about the mix of part time vs full time workers imo. $\endgroup$ – Hessian Dec 15 '16 at 13:17
  • $\begingroup$ @Hessian I really don't know, I'm kinda just fumbling around on google scholar trying to figure out If Roberts's law works. It seems like an odd formula to me and this is the only measure of firm size I've found so far. $\endgroup$ – EconJohn Dec 15 '16 at 16:55
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There are plenty of papers studying CEO pay and firm size empirically. Check a long list here. Some examples of data sources:

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